19 research outputs found
Star product and the general Leigh-Strassler deformation
We extend the definition of the star product introduced by Lunin and
Maldacena to study marginal deformations of N=4 SYM. The essential difference
from the latter is that instead of considering U(1)xU(1) non-R-symmetry, with
charges in a corresponding diagonal matrix, we consider two Z_3-symmetries
followed by an SU(3) transformation, with resulting off-diagonal elements. From
this procedure we obtain a more general Leigh-Strassler deformation, including
cubic terms with the same index, for specific values of the coupling constants.
We argue that the conformal property of N=4 SYM is preserved, in both beta-
(one-parameter) and gamma_{i}-deformed (three-parameters) theories, since the
deformation for each amplitude can be extracted in a prefactor. We also
conclude that the obtained amplitudes should follow the iterative structure of
MHV amplitudes found by Bern, Dixon and Smirnov.Comment: 21 pages, no figures, JHEP3, v2: references added, v3: appendix A
added, v4: clarification in section 3.
Open Spin Chains in Super Yang-Mills at Higher Loops: Some Potential Problems with Integrability
The super Yang-Mills duals of open strings attached to maximal giant
gravitons are studied in perturbation theory. It is shown that non-BPS baryonic
excitations of the gauge theory can be studied within the paradigm of open
quantum spin chains even beyond the leading order in perturbation theory. The
open spin chain describing the two loop mixing of non-BPS giant gravitons
charged under an su(2) of the so(6) R symmetry group is explicitly constructed.
It is also shown that although the corresponding open spin chain is integrable
at the one loop order, there is a potential breakdown of integrability at two
and higher loops. The study of integrability is performed using coordinate
Bethe ansatz techniques.Comment: 28 pages. References added in revised versio
The general Leigh-Strassler deformation and integrability
The success of the identification of the planar dilatation operator of N=4
SYM with an integrable spin chain Hamiltonian has raised the question if this
also is valid for a deformed theory. Several deformations of SYM have recently
been under investigation in this context. In this work we consider the general
Leigh-Strassler deformation. For the generic case the S-matrix techniques
cannot be used to prove integrability. Instead we use R-matrix techniques to
study integrability. Some new integrable points in the parameter space are
found.Comment: 22 pages, 8 figures, reference adde
Yangians in Deformed Super Yang-Mills Theories
We discuss the integrability structure of deformed, four-dimensional N=4
super Yang-Mills theories using Yangians. We employ a recent procedure by
Beisert and Roiban that generalizes the beta deformation of Lunin and Maldacena
to produce N=1 superconformal gauge theories, which have the superalgebra
SU(2,2|1)xU(1)xU(1). The deformed theories, including those with the more
general twist, were shown to have retained their integrable structure. Here we
examine the Yangian algebra of these deformed theories. In a five field
subsector, we compute the two cases of SU(2)xU(1)xU(1)xU(1) and
SU(2|1)xU(1)xU(1) as residual symmetries of SU(2,2|1)xU(1)xU(1). We compute a
twisted coproduct for these theories, and show that only for the residual
symmetry do we retain the standard coproduct. The twisted coproduct thus
provides a method for symmetry breaking. However, the full Yangian structure of
SU(2|3) is manifest in our subsector, albeit with twisted coproducts, and
provides for the integrability of the theory.Comment: 17 page
Quantum Symmetries and Marginal Deformations
We study the symmetries of the N=1 exactly marginal deformations of N=4 Super
Yang-Mills theory. For generic values of the parameters, these deformations are
known to break the SU(3) part of the R-symmetry group down to a discrete
subgroup. However, a closer look from the perspective of quantum groups reveals
that the Lagrangian is in fact invariant under a certain Hopf algebra which is
a non-standard quantum deformation of the algebra of functions on SU(3). Our
discussion is motivated by the desire to better understand why these theories
have significant differences from N=4 SYM regarding the planar integrability
(or rather lack thereof) of the spin chains encoding their spectrum. However,
our construction works at the level of the classical Lagrangian, without
relying on the language of spin chains. Our approach might eventually provide a
better understanding of the finiteness properties of these theories as well as
help in the construction of their AdS/CFT duals.Comment: 1+40 pages. v2: minor clarifications and references added. v3: Added
an appendix, fixed minor typo
Giants On Deformed Backgrounds
We study giant graviton probes in the framework of the three--parameter
deformation of the AdS_5 x S^5 background. We examine both the case when the
brane expands in the deformed part of the geometry and the case when it blows
up into AdS. Performing a detailed analysis of small fluctuations around the
giants, the configurations turn out to be stable. Our results hold even for the
supersymmetric Lunin-Maldacena deformation.Comment: LaTex, 28 pages, uses JHEP3; v2: minor corrections, references added;
v3: final version accepted for publication in JHE
On the perturbative chiral ring for marginally deformed N=4 SYM theories
For \cal{N}=1 SU(N) SYM theories obtained as marginal deformations of the
\cal{N}=4 parent theory we study perturbatively some sectors of the chiral ring
in the weak coupling regime and for finite N. By exploiting the relation
between the definition of chiral ring and the effective superpotential we
develop a procedure which allows us to easily determine protected chiral
operators up to n loops once the superpotential has been computed up to (n-1)
order. In particular, for the Lunin-Maldacena beta-deformed theory we determine
the quantum structure of a large class of operators up to three loops. We
extend our procedure to more general Leigh-Strassler deformations whose chiral
ring is not fully understood yet and determine the weight-two and weight-three
sectors up to two loops. We use our results to infer general properties of the
chiral ring.Comment: LaTex, 40 pages, 4 figures, uses JHEP3; v2: minor correction
Green-Schwarz Strings in TsT-transformed backgrounds
We consider classical strings propagating in a background generated by a
sequence of TsT transformations. We describe a general procedure to derive the
Green-Schwarz action for strings. We show that the U(1) isometry variables of
the TsT-transformed background are related to the isometry variables of the
initial background in a universal way independent of the details of the
background. This allows us to prove that strings in the TsT-transformed
background are described by the Green-Schwarz action for strings in the initial
background subject to twisted boundary conditions. Our construction implies
that a TsT transformation preserves integrability properties of the string
sigma model. We discuss in detail type IIB strings propagating in the
\g_i-deformed AdS_5 x S^5 space-time, find the twisted boundary conditions for
bosons and fermions, and use them to write down an explicit expression for the
monodromy matrix. We also discuss string zero modes whose dynamics is governed
by a fermionicgeneralization of the integrable Neumann model.Comment: 33 pages, latex, v2: typos correcte
Four-loop anomalous dimensions in Leigh-Strassler deformations
We determine the scalar part of the four-loop chiral dilatation operator for
Leigh-Strassler deformations of N=4 super Yang-Mills. This is sufficient to
find the four-loop anomalous dimensions for operators in closed scalar
subsectors. This includes the SU(2) subsector of the (complex)
beta-deformation, where we explicitly compute the anomalous dimension for
operators with a single impurity. It also includes the "3-string null"
operators of the cubic Leigh-Strassler deformation. Our four-loop results show
that the rational part of the anomalous dimension is consistent with a
conjecture made in arXiv:1108.1583 based on the three-loop result of
arXiv:1008.3351 and the N=4 magnon dispersion relation. Here we find additional
zeta(3) terms.Comment: Latex, feynmp, 21 page
Supergraphs and the cubic Leigh-Strassler model
We discuss supergraphs and their relation to "chiral functions" in N=4 Super
Yang-Mills. Based on the magnon dispersion relation and an explicit three-loop
result of Sieg's we make an all loop conjecture for the rational contributions
of certain classes of supergraphs. We then apply superspace techniques to the
"cubic" branch of Leigh-Strassler N=1 superconformal theories. We show that
there are order 2^L/L single trace operators of length L which have zero
anomalous dimensions to all loop order in the planar limit. We then compute the
anomalous dimensions for another class of single trace operators we call
one-pair states. Using the conjecture we can find a simple expression for the
rational part of the anomalous dimension which we argue is valid at least up to
and including five-loop order. Based on an explicit computation we can compute
the anomalous dimension for these operators to four loops.Comment: 22 pages; v2: Conjecture modified to apply only for the rational part
of the chiral functions. Typos fixed. Minor modification